Clamp velocity along local axis
You're on the right track with your setup. What you want to avoid, is the overshoot you get when turning. This can be controlled with the linear ("Translation") and angular ("Rotation") damping:



Once you increase those values, as in this screenshot, you'll get much closer to the behaviour you're looking for. You probably also need to increase the velocities in your logic bricks, to compensate for the loss in speed due to the damping.